‎In this paper‎, ‎we define the common minimal common neighborhood‎ ‎dominating signed graph (or common minimal $CN$-dominating signed‎ ‎graph) of a given signed graph and offer a structural‎ ‎characterization of common minimal $CN$-dominating signed graphs‎. ‎In the sequel‎, ‎we also obtained switching equivalence‎
‎characterization‎: ‎$\overline{\Sigma} \sim CMCN(\Sigma)$‎, ‎where‎ ‎$\overline{\Sigma}$ and $CMCN(\Sigma)$ are complementary signed‎ ‎graph and common minimal $CN$-signed graph of $\Sigma$‎ ‎respectively‎.